Raman lasers based on integrated silica whispering gallery mode resonant cavities have enabled numerous applications from telecommunications to biodetection. To overcome the intrinsically low Raman gain value of silica, these devices leverage their ultra-high quality factors (Q), allowing sub-mW stimulated Raman scattering (SRS) lasing thresholds to be achieved. A closely related nonlinear behavior to SRS is stimulated anti-Stokes Raman scattering (SARS). This nonlinear optical process combines the pump photon with the SRS photon to generate an upconverted photon. Therefore, in order to achieve SARS, the efficiency of the SRS process must be high. As a result, achieving SARS in on-chip resonant cavities has been challenging due to the low lasing efficiencies of these devices. In the present work, metal-doped ultra-high Q (Q>107) silica microcavity arrays are fabricated on-chip. The metal-dopant plays multiple roles in improving the device performance. It increases the Raman gain of the cavity material, and it decreases the optical mode area, thus increasing the circulating intensity. As a result, these devices have SRS lasing efficiencies that are over 10x larger than conventional silica microcavities while maintaining low lasing thresholds. This combination enables SARS to be generated with sub-mW input powers and significantly improved anti-Stokes Raman lasing efficiency.
Blood analysis is an important diagnostic tool, as it provides a wealth of information about the patient health. Raman spectroscopy is a promising tool in blood analysis, but widespread clinical application is limited by its low signal strength, as well as complex and costly instrumentation. The growing field of waveguide-based Raman spectroscopy tries to solve these challenges by working towards fully integrated Raman sensors with increased interaction areas. In this work, we demonstrate on-chip resonance Raman measurements of hemoglobin, a crucial component of blood, at 532 nm excitation usi…
Noble-metal-free surface-enhanced Raman scattering (SERS) substrates have attracted great attention for their abundant sources, good signal uniformity, superior biocompatibility, and high chemical stability. However, the lack of controllable synthesis and fabrication of noble-metal-free substrates with high SERS activity impedes their practical applications. Herein,we propose a general strategy to fabricate a series of planar transition-metal nitride (TMN) SERS chips via an ambient temperature sputtering deposition route.These planar TMN (tungsten nitride, tantalum nitride, and molybdenum nitr…
We demonstrate stimulated Raman gain using a broadband LED Stokes source to measure vibrational spectra of aqueous glucose solutions. This versatile and cost-effective method increases Raman signal for a variety of applications. We measured both stimulated Raman and spontaneous Raman spectra of glucose solutions with concentrations up to 10 mM with a photon counter and lock-in amplifier. We built partial least squares regression models based on both stimulated Raman and spontaneous Raman spectral data measured with each instrument for predicting concentrations of the glucose solutions. The sti…
Waveguide-enhanced Raman spectroscopy (WERS) is a promising technique for sensitive and selective detection of chemicals in a compact chip-scale platform. Coupling light on and off the sensor chip with fibers however presents challenges because of the fluorescence and Raman background generated by the pump light in the fibers; as a result all WERS demonstrations to date have used free-space coupling via lenses. We report a packaged, fiber-bonded WERS chip that filters the background on-chip through collection of the backscattered Raman light. The packaged sensor is integrated in a ruggedized f…
The polarization of light conveys unique information that can be exploited by crucial applications. The bulky and costly discrete optical components used in conventional polarimeters limit their broad adoption. A compact, low-cost polarimeter would bring this functionality into a myriad of new scenarios and revolutionize its exploitation. Here we present a high-performance, full-Stokes polarimeter on a silicon chip. A surface polarization splitter and on-chip optical interferometer circuit produce the analysis matrix of an optimally conditioned polarimeter. This solid-state polarimeter is a sy…
The noise figure and photon probability distribution are calculated for coherent anti-Stokes Raman scattering (CARS) where an anti-Stokes signal is converted to Stokes. We find that the minimum noise figure is ~ 3dB.
We propose an integrated surface enhanced Raman scattering (SERS) chip based on liquid-core waveguide with total reflection, through which the depression of leaky mode enable a long propagating distance. An Raman enhancement factor for rhodamine 6G of 2.5*105 is obtained, and a excellent repeatability is shown. The peaks in the SERS spectrum of DNA of silkworm clearly illustrate the information of the molecule structure. The integration of the SERS substrate, micro-fluid, and liquid-core waveguide make such a SERS chip attractive for biochemical detection with high performance.
Polarimetric imaging has a wide range of applications for uncovering features invisible to human eyes and conventional imaging sensors. Compact, fast, cost-effective and accurate full-Stokes polarimetric imaging sensors are highly desirable in many applications, which, however, remain elusive due to fundamental material limitations. Here we present a Metasurface-based Full-Stokes Polarimetric Imaging sensor (MetaPolarIm) realized by integrating an ultrathin (~600 nm) metasurface polarization filter array (MPFA) onto a visible imaging sensor with CMOS compatible fabrication processes. The MPFA …
We present general analytical expressions of Stokes and anti-Stokes spectral photon-flux densities that are spontaneously generated by a single monochromatic pump wave propagating in a single-mode optical fiber. We validate our results by comparing them with experimental data. Limiting cases of the general expressions corresponding to interesting physical situations are discussed.
We show that coherent anti-Stokes Raman lineshapes do not follow known spectral profiles if the time asymmetry of realistic laser pulses is taken into account. Examples are given for nanosecond and picosecond laser pulses commonly employed in frequency-resolved coherent anti-Stokes Raman scattering. More remarkably, the analysis suggests an effect of line narrowing in comparison to the customary approach, based primarily on the Voigt lineshape.
We review an on-chip approach for spontaneous Raman spectroscopy and Surface Enhanced Raman Spectroscopy (SERS) based on evanescent excitation of the analyte as well as evanescent collection of the Raman signal using Complementary Metal Oxide Semiconductor (CMOS) compatible single mode waveguides. The signal is either directly collected from the analyte molecules or via plasmonic nanoantennas integrated on top of the waveguides. Flexibility in the design of the geometry of the waveguide, and/or the geometry of the antennas, enables optimization of the collection efficiency. Furthermore the sen…
We propose a full-vectorial numerical study of far field radiation patterns in coherent anti-Stokes Raman scattering (CARS) microscopy. We emphasis the particular role of the Raman depolarisation ratio of the observed medium and show how it modifies the radiation pattern of thin objects.
We introduce new lineshapes of coherent anti-Stokes Raman spectra of gases by considering realistic nanosecond laser pulses that deviate from the Gaussian representations of their time and spectral envelopes. The analysis suggests that the contribution to the linewidth caused by the interaction with such laser pulses could be erroneously attributed to the intrinsic Raman width if the customary CARS approach, based primarily on the Voigt lineshape, is assumed.
We have developed an interferometric implementation of coherent anti-Stokes Raman scattering (CARS) which enables broadband coherent Raman spectroscopy free from non-resonant background (NRB), with a signal strength proportional to concentration. Spectra encode mode symmetry information into the amplitude response which can be directly compared to polarised spontaneous Raman spectra. The method requires only passive polarisation optics and is suitable for a wide range of laser linewidths and pulse durations
We show that time-resolved coherent anti-Stokes Raman signals of isolated transitions deviate from the exponential decay whose time constant is nowadays used for measuring Raman linewidths. The deviation is caused by probe pulse-shape effects that can be understood in terms of the spectral filtering created by the necessary action of laser probing. Consequent corrections to recent linewidth measurements on heteronuclear molecules support the unprecedented agreement between theoretical works and experiments.
Coherent Raman scattering spectroscopy is studied purposely, with the Gaussian ultrashort pulses as a hands-on elucidatory extraction tool of the clean coherent Raman resonant spectra from the overall measured data contaminated with the non-resonant four wave mixing background. The integral formulae for both the coherent anti-Stokes and Stokes Raman scattering are given in the semiclassical picture, and the closed-form solutions in terms of a complex error function are obtained. An analytic form of maximum enhancement of pure coherent Raman spectra at threshold time delay depending on bandwidt…
Due to their high circulating intensities, ultra-high quality factor dielectric whispering-gallery mode resonators have enabled the development of low threshold Raman microlasers. Subsequently, other Raman-related phenomena, such as cascaded stimulated Raman scattering (CSRS) and stimulated anti-Stokes Raman scattering (SARS), were observed. While low threshold frequency conversion and generation have clear applications, CSRS and SARS have been limited by the low Raman gain. In this work, the surface of a silica resonator is modified with an organic monolayer, increasing the Raman gain. Up to …
Synthetic single-crystal diamond has recently emerged as a promising platform for Raman lasers at exotic wavelengths due to its giant Raman shift, large transparency window and excellent thermal properties yielding a greatly enhanced figure-of-merit compared to conventional materials. To date, diamond Raman lasers have been realized using bulk plates placed inside macroscopic cavities, requiring careful alignment and resulting in high threshold powers (~W-kW). Here we demonstrate an on-chip Raman laser based on fully-integrated, high quality-factor, diamond racetrack micro-resonators embedded …
We propose to use frequency-selective quasi parity-time symmetry to reduce the heat generated by coherent anti-Stokes Raman scattering (CARS) reversed cycles in active Raman media with phase mismatch. This is accomplished using a coupled-waveguide structure, which includes the active Raman waveguide (RW), where the Stokes signal undergoes amplification via stimulated Stokes Raman scattering (SSRS), and a dissipative waveguide (DW), which is tuned to the anti-Stokes wavelength so as to evacuate the corresponding anti-Stokes photons from the RW by coupling. The DW introduces optical loss that pa…
We propose an elegant scheme towards phase locking of two independent degenerate coherent anti-Stokes Raman scattering (CARS) processes. The optical implementation involves a modified Mach-Zehnder interferometer that is utilized to transfer phase coherence from three totally uncorrelated laser beams into two degenerate CARS beams which are independently produced in two distinct Raman active samples. Such a phase-transport interferometer allows for explicit measurement and control of phase differences between the two phase-locked degenerate CARS processes, hence may lead to applications in othe…
We theoretically investigate a scheme in which backward coherent anti-Stokes Raman scattering (CARS) is significantly enhanced by using slow light. Specifically, we reduce the group velocity of the Stokes excitation pulse by introducing a coupling laser that causes electromagnetically induced transparency (EIT). When the Stokes pulse has a spatial length shorter than the CARS wavelength, the backward CARS emission is significantly enhanced. We also investigated the possibility of applying this scheme as a CARS lidar with O2 or N2 as the EIT medium. We found that if nanosecond laser with large …
Single-shot time resolved Coherent Anti-Stokes Raman Scattering (CARS) is presented as a viable method for fast measurements of molecular spectra. The method is based on the short spatial extension of femtosecond pulses and maps time delays between pulses onto the region of intersection between broad beams. The image of the emitted CARS signal contains full temporal information on the field-free molecular dynamics, from which spectral information is extracted. The method is demonstrated on liquid samples of CHBr3 and CHCl3 and the Raman spectrum of the low-lying vibrational states of these mol…
The spectral resolution of broadband Fourier-transform coherent anti-Stokes Raman spectroscopy is limited by the maximum optical path length difference that can be scanned within a short time in an interferometer. However, alternatives to the Fourier-transform exist which can bypass this limitation with certain assumptions. We apply one such approach to broadband coherent Raman spectroscopy using interferometers with short delay line (low Fourier spectral resolution) and large delay line (high Fourier spectral resolution). With this method, we demonstrate broadband coherent Raman spectroscopy …
We experimentally demonstrate efficient Raman conversion to respective Stokes and anti-Stokes fields in both pulsed and continuous modes with a Rb-87 atomic vapor cell. The conversion efficiency is about 40-50% for the Stokes field and 20-30% for the anti-Stokes field, respectively. This conversion process is realized with feedback of both the Raman pump and the frequency-converted fields (Stokes or anti-Stokes). The experimental setup is very simple and can be applied easily to produce the light source with larger frequency difference using other Raman media. They may have wide applications i…
We demonstrate a novel technique of coherent Raman spectroscopy with a femtosecond laser. We apply to a molecular sample a sequence of pairs of ultrashort excitation and probe pulses, with a linearly increasing time delay between the two pulses from one pair to the next. We measure, as a function of the delay, the intensity modulation in the signal resulting from the differential detection of the Stokes and anti-Stokes radiations generated at the sample. The Fourier transform of such time-domain signal reveals the spectrum of the excited vibrational Raman transitions. The experimental proof-of…
We propose a new technique for comparing two Raman active samples. The method employs optical interference of the signals generated via coherent anti-Stokes Raman scattering (CARS) of broadband laser pulses with noisy spectra. It does not require spectrally resolved detection, and no prior knowledge about either the Raman spectrum of the samples, or the spectrum of the incident light is needed. We study the proposed method theoretically, and demonstrate it in a proof-of-principle experiment on Toluene and ortho-Xylene samples.
We demonstrate for the first time, Raman random lasing in a continuous-wave (CW) excited, completely biocompatible and biodegradable carrot medium. The Stokes Raman mode of carotene renders carrot as a gain medium whereas random scattering in the natural fibrous cellulose of the carrot structure facilitates random lasing. CW laser induced photoluminescence(PL) threshold and linewidth analysis at the Stokes modes of carotene show a characteristic lasing action with threshold of 130 W/cm2 and linewidth-narrowing with mode Q factors (~1300). Polarization study of output modes reveals that lasing …
We show that the increasingly popular nonlinear optical technique of time-domain coherent anti-Stokes Raman scattering (CARS), which is usually understood in terms of the semiclassical time-dependent third-order polarization, can be equally explained in terms of the time-delayed version of the Yuratich equation so popular in traditional frequency-domain CARS. The method brings out the strong dependence of CARS time traces and time-delayed CARS lineshapes on the spectral envelope of the probe laser electric field. Examples are analytically shown for experimental results that are otherwise treat…
Nonlinear optical methods, such as coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS), are able to perform label free imaging, with chemical bonds specificity. Here, we demonstrate that the use of circularly polarized light allows to retrieve not only the chemical nature but also the symmetry of the probed sample, in a single shot measurement. Our symmetry-resolved scheme offers simple access to the local organization of vibrational bonds and as a result provides enhanced image contrast for anisotropic samples as well as an improved chemical selectivity. We quan…
Wavelength-dependent polarization state of light carries crucial information about light-matter interactions. However, its measurement is limited to bulky, energy-consuming devices, which prohibits many modern, portable applications. Here, we propose and demonstrate a chip-scale spectropolarimeter implemented using a CMOS-compatible silicon photonics technology. Four compact Vernier microresonator spectrometers are monolithically integrated with a broadband polarimeter consisting of a 2D nanophotonic antenna and a polarimetric circuit to achieve full-Stokes spectropolarimetric analysis. The pr…
Since its first demonstration in the sixties, coherent anti-Stokes Raman scattering (CARS) has become a powerful spectroscopic sensing tool with broad applications in biology and chemistry. However, it is a complex nonlinear optical process that often leads to the lacks of quantitative data outputs. In this letter, we observe how CARS signal builds up gradually and demonstrate how to control its deferral with laser-pulse shaping. A time-resolved three-color CARS that involves a pair of driving broadband femtosecond pulses and delayed shaped probe pulse is realized experimentally. Driving pulse…
We study Raman scattering in active media placed in proximity of different types of metal nanostructures, at wavelengths that display either Fabry-Perot or plasmonic resonances, or a combination of both. We use a semi-classical approach to derive equations of motion for Stokes and anti-Stokes fields that arise from quantum fluctuations. Our calculations suggest that local field enhancement yields Stokes and anti-Stokes conversion efficiencies between five and seven orders of magnitudes larger compared to cases without the metal nanostructure. We also show that to first order in the linear susc…
The operator solution of a completely quantum mechanical Hamiltonian of the Raman processes is used here to investigate the possibility of obtaining intermodal entanglement between different modes involved in the Raman processes (e.g. pump mode, Stokes mode, vibration (phonon) mode and anti-Stokes mode). Intermodal entanglement is reported between a) pump mode and anti-Stokes mode, b) pump mode and vibration (phonon) mode c) Stokes mode and vibration phonon mode, d) Stokes mode and anti-stokes mode in the stimulated Raman processes for the variation of the phase angle of complex eigenvalue $α_…
We report stimulated Raman spectroscopy of the G phonon in both single and multi-layer graphene, through Coherent anti-Stokes Raman Scattering (CARS). The signal generated by the third order nonlinearity is dominated by a vibrationally non-resonant background (NVRB), which obscures the Raman lineshape. We demonstrate that the vibrationally resonant CARS peak can be measured by reducing the temporal overlap of the laser excitation pulses, suppressing the NVRB. We model the observed spectra, taking into account the electronically resonant nature of both CARS and NVRB. We show that CARS can be us…
We investigate the arrival statistics of Stokes (S) and anti-Stokes (aS) Raman photons generated in diamond membranes. Strong quantum correlations between the S and aS signals are observed, which implies that the two processes share the same phonon, that is, the phonon excited by the S process is consumed in the aS process. We show that the intensity cross-correlation $g_{\rm S,aS}^{(2)}(0)$, which describes the simultaneous detection of Stokes and anti-Stokes photons, decreases steadily with laser power as $1/{\rm P_L}$. Contrary to many other material systems, diamond exhibits a maximum $g_{…
Chalcogenide glass (ChG) is an attractive material for integrated nonlinear photonics due to its wide transparency and high nonlinearity, and its capability of being directly deposited and patterned on Silicon wafer substrates. It has a singular Raman effect among amorphous materials. Yet, the Raman lasing performance in high quality and chip integrated ChG microresonators remains unexplored. Here, we demonstrate an engineered Raman lasing dynamic based on home developed photonic integrated high-Q ChG microresonators. With a quality factor above 10^6, we achieve the record-low lasing threshold…
Multimode hollow microcavities in three-dimensional (3D) photonic crystals (PhCs) are designed for achieving enhanced coherent anti-Stokes Raman scattering, which requires a cavity to have three high quality-factor (Q) modes with equally spaced resonant frequencies. Cavities in 3D PhCs allows more flexibility in design and tuning than their 2D slab counterparts, since radiation loss that degrades Q can be suppressed by the 3D photonic band gap. We first tune all the mode frequencies simultaneously by changing the material and geometry of the cavity based on perturbation theory. Spectral spacin…
Compact, power efficient and fiber compatible lasers, wavelength converters and amplifiers are vital ingredients for the future fiber optic systems and networks. Nonlinear optical effects, like Raman scattering and parametric four wave mixing, offer a way to realize such devices. Here we use a single chalcogenide microwire to realize a device that provides the functions of a Stokes Raman parametric laser, a four wave mixing anti Stokes wavelength converter, and an ultra broadband Stokes/anti Stokes Raman amplifier or supercontinuum generator. The device operation relies on ultrahigh Raman and …
Far field radiation pattern under tight focusing condition is investigated in Coherent Anti-stokes Raman Scattering (CARS) microscopy both in the forward (F-CARS) and backward (E-CARS) directions. While we assume no refraction index mismatch between the sample and the environing medium, our rigorous numerical electromagnetic computation takes into account the exact polarizations of the excitation laser beams and of the induced nonlinear dipoles. F-CARS and E-CARS radiation patterns, as well as their divergence, are studied as a function of the size of the sample object and compared to the exci…
Coherent Raman microscopy provide label-free imaging by interrogating the intrinsic vibration of biomolecules. Nevertheless, trade-off between high chemical-specificity and high imaging-speed currently exists in transition from spectroscopy to spectroscopic imaging when capturing dynamics in complex living systems. Here, we present a novel concept in dual-comb scheme to substantially beat this trade-off and facilitate high-resolution broadband coherent anti-Stokes Raman spectroscopic imaging based on down-converted, automatically varying delay-time in spectral focusing excitation. A rapid meas…
A major impediment of using Coherent Anti-Stokes Raman Scattering to identify biological molecules is that the illumination levels required to produce a measurable signal often also produce significant nonresonant background from the medium, especially from water, that is not specific to the resonance being investigated. We present a method of using nonlinear interferometry to measure the temporal shape of the anti-Stokes signal to differentiate which components are resonant and nonresonant. This method is easily adaptable to most existing pulsed CARS illumination methods and should allow for …
Surface-enhanced coherent anti-Stokes Raman scattering (SE-CARS) takes advantage of surface plasmon resonances supported on metallic nanostructures to amplify the coherent Raman response of target molecules. While these metallic antennas have found significant success in SE-CARS studies, photo-induced morphological changes to the nanoantenna under ultrafast excitation introduce significant hurdles in terms of stability and reproducilibty. These hurdles need to be overcome in order to establish SE-CARS as a reliable tool for rapid biomolecular sensing. Here we address this challenge by performi…
We propose an all-fiber-generated dual-soliton pulses based scheme for the background-free detection of coherent anti-Stokes Raman spectroscopy under the spectral focusing mechanism. Due to the strong birefringence and high nonlinearity of a polarization-maintaining photonic crystal fiber (PM-PCF), two redshifted soliton pulses can be simultaneously generated relying on high-order dispersion and nonlinear effects along two eigenpolarization axes in the anomalous dispersion regime, while allowing feasible tunability of the frequency distance and temporal interval between them. This proposed sch…
A new interferometric technique is demonstrated for measuring Coherent Anti-Stokes Raman Scattering (CARS) signals. Two forward-directed CARS signals are generated, one in each arm of an interferometer. The deterministic nature of the CARS process allows for these two signals, when spatially and temporally overlapped, to interfere with one another. Heterodyne detection can therefore be employed to increase the sensitivity in CARS signal detection. In addition, nonlinear CARS interferometry will facilitate the use of this spectroscopic technique for molecular contrast in Optical Coherence Tomog…
Coherent Anti-Stokes Raman Scattering (CARS) processes are ``coherent,'' but the phase of the anti-Stokes radiation is usually lost by most incoherent spectroscopic CARS measurements. We propose a novel Raman microscopy imaging method called Nonlinear Interferometric Vibrational Imaging, which measures Raman spectra by obtaining the temporal anti-Stokes signal through nonlinear interferometry. With a more complete knowledge of the anti-Stokes signal, we show through simulations that a high-resolution Raman spectrum can be obtained of a molecule in a single pulse using broadband radiation. This…
We present a self-consistent quantum optics approach to calculating the surface enhanced Raman spectrum of molecules coupled to arbitrarily shaped plasmonic systems. Our treatment is intuitive to use and provides fresh analytical insight into the physics of the Raman scattering near metallic surfaces and can be applied to a wide range of geometries including resonators, waveguides, as well as hybrid photonic-plasmonic systems. Our general theory demonstrates that the detected Raman spectrum originates from an interplay between nonlinear light generation and propagation. Counter intuitively, at…
We report the observations of spontaneous Raman scattering in silicon photonic crystal waveguides. Continuous-wave measurements of Stokes emission for both wavelength and power dependence is reported in single line-defect waveguides in hexagonal lattice photonic crystal silicon membranes. By utilizing the Bragg gap edge dispersion of the TM-like mode for pump enhancement and the TE-like fundamental mode-onset for Stokes enhancement, the Stokes emission was observed to increase by up to five times in the region of slow group velocity. The results show explicit nonlinear enhancement in a silicon…
We formulate a generic concept of engineering optical modes and mechanical resonances in a pair of optically-coupled light-guiding membranes for achieving cascaded light scattering to multiple Stokes and anti-Stokes orders. By utilizing the light pressure exerted on the webs and their induced flexural vibrations, featuring flat phonon dispersion curve with a non-zero cut-off frequency, we show how to realize exact phase-matching between multiple successive optical side-bands. We predict continuous-wave generation of frequency combs for fundamental and high-order optical modes mediated via back…
The temperature dependence of the asymmetry between Stokes and anti-Stokes Raman scattering can be exploited for self-calibrating, optically-based thermometry. In the context of cavity optomechanics, we observe the cavity-enhanced scattering of light interacting with the standing-wave drumhead modes of a silicon nitride membrane mechanical resonator. The ratio of the amplitude of Stokes to anti-Stokes scattered light is used to measure temperatures of optically-cooled mechanical modes down to the level of a few vibrational quanta. We demonstrate that the Raman-ratio technique is able to measur…
Optical refrigeration of solids holds tremendous promise for applications in thermal management. It can be achieved through multiple mechanisms including inelastic anti-Stokes Brillouin and Raman scattering. However, engineering of these mechanisms remains relatively unexplored. The major challenge lies in the natural unfavorable imbalance in transition rates for Stokes and anti-Stokes scattering. We consider the influence of anisotropic photonic density of states on Raman scattering and derive expressions for cooling in such systems. We demonstrate optimization of the Raman cooling figure of …
We investigate the evolution of coherence property of noise-seeded Stokes wave in short (< 1 ps) and long pulse (> 1 ps) regimes. Nonlinear equations expressing the evolution of pump and Stokes wave are solved numerically for both the regions. The simulations include quantum noise by incorporating noise seed in the pump field where one photon per mode with random phase. The spectral phase fluctuations of the Stokes wave for both the regions, are characterized by performing multiple simulations and finally, the degrees of first-order mutual coherence are calculated as a function of wavelength f…
